scholarly journals A duality theorem in Hopf algebras and its application to Morava K-theory of $B\mathbf{Z}/p^r$

1996 ◽  
Vol 36 (4) ◽  
pp. 771-778
Author(s):  
Kakhaber Kordzaya ◽  
Goro Nishida
Keyword(s):  
Hopf Algebras ◽  
Duality Theorem ◽  
K Theory

scholarly journals Antipode Formulas for some Combinatorial Hopf Algebras

10.37236/5949 ◽  
2016 ◽  
Vol 23 (4) ◽  
Author(s):  
Rebecca Patrias
Keyword(s):  
Hopf Algebra ◽  
Hopf Algebras ◽  
Symmetric Functions ◽  
Explicit Formulas ◽  
Quasisymmetric Functions ◽  
Noncommutative Symmetric Functions ◽  
Combinatorial Hopf Algebras ◽  
Combinatorial Formulas ◽  
K Theory

Motivated by work of Buch on set-valued tableaux in relation to the K-theory of the Grassmannian, Lam and Pylyavskyy studied six combinatorial Hopf algebras that can be thought of as K-theoretic analogues of the Hopf algebras of symmetric functions, quasisymmetric functions, noncommutative symmetric functions, and of the Malvenuto-Reutenauer Hopf algebra of permutations. They described the bialgebra structure in all cases that were not yet known but left open the question of finding explicit formulas for the antipode maps. We give combinatorial formulas for the antipode map for the K-theoretic analogues of the symmetric functions, quasisymmetric functions, and noncommutative symmetric functions.

Hopf Algebras of Cooperations for Real and Complex K -Theory

1971 ◽  
Vol s3-23 (3) ◽  
pp. 385-408 ◽  
Author(s):  
J. F. Adams ◽  
A. S. Harris ◽  
R. M. Switzer
Keyword(s):  
Hopf Algebras ◽  
K Theory

scholarly journals A duality theorem for weak multiplier Hopf algebra actions

2017 ◽  
Vol 28 (05) ◽  
pp. 1750032 ◽  
Author(s):  
Nan Zhou ◽  
Shuanhong Wang
Keyword(s):  
Hopf Algebra ◽  
Hopf Algebras ◽  
Duality Theorem ◽  
Smash Product ◽  
Module Algebra ◽  
Multiplier Hopf Algebras ◽  
Multiplier Hopf Algebra ◽  
Weak Hopf Algebras

The main purpose of this paper is to unify the theory of actions of Hopf algebras, weak Hopf algebras and multiplier Hopf algebras to one of actions of weak multiplier Hopf algebras introduced by Van Daele and Wang. Using such developed actions, we will define the notion of a module algebra over weak multiplier Hopf algebras and construct their smash products. The main result is the duality theorem for actions and their dual actions on the smash product of weak multiplier Hopf algebras. As an application, we recover the main results found in the literature for weak Hopf algebras, multiplier Hopf algebras and groupoids.

The duality theorem for twisted smash products of Hopf algebras and its applications

2015 ◽  
Vol 141 (1) ◽  
pp. 25-44
Author(s):  
Zhongwei Wang ◽  
Liangyun Zhang
Keyword(s):  
Hopf Algebras ◽  
Duality Theorem

An Introduction to K-Theory for C*-Algebras

2000 ◽  
Author(s):  
M. Rørdam ◽  
F. Larsen ◽  
N. Laustsen
Keyword(s):  
C Algebras ◽  
K Theory
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